The minor was last seen with a youth from her locality before she went missing on Thursday, they said.
Police said they were alerted by a neighbour of the girl when he saw her on fire and screaming at the spot yesterday.
She was rushed to Government Medical College hospital where doctors said she had sustained 90 per cent burn injuries.
"The girl died in the wee hours today," police said.
They were exploring possibilities like rape, suicide and kidnapping as probable reasons behind the incident. They are also awaiting the post-mortem report.